Electrode kinetics Tafel plot

If we want to use the Tafel slopes to obtain the empirical kinetics of polymerization, we have to use a metallic electrode coated with a previously electrogenerated thin and uniform film of the polymer in a fresh solution of the monomer. In some cases experimental Tafel plots present the two components (Fig. 4) before and after coating. 

Figure 4. Log intensity vs. potential plots (Tafel plots) obtained from the voltammograms of a platinum electrode submitted to a 2 mV s l potential sweep polarized in a 0.1 M LiC104 acetonitrile solution having different thiophene concentrations. (Reprinted from T. F. Otero and J. Rodriguez, Parallel kinetic studies of the electrogeneration of conducting polymers mixed materials, composition, and kinetic control. Electrochim, Acta 39, 245, 1994, Figs. 2, 7. Copyright 1997. Reprinted with permission from Elsevier Science.)...

To make Tafel plots (Figure 8.15) [124,125] subsequent to the subtraction of the ohmic losses (iR), the electrode overpotential, p, is plotted versus ln(.//./0). For systems controlled by standard electrochemical kinetics, the slope at a high overpotential gives the anodic and the cathodic transference coefficients, aA and ac, respectively, and the intercept gives the exchange current density, J0. 

An example of the size of the impurity effects that may arise is shown in Fig. 1, which gives the electrode kinetics for the ferro-ferricyanide reaction on three different zinc oxide single crystals of varying conductivity. Each of the crystals was in excess of 99.999% pure. As can be seen, each crystal gives a linear Tafel plot under cathodic bias. However, the exchange currents, i.e, the extrapolations back to the reversible potential (+. 19 volts), differ by a factor of about 1000 and... 

The Tafel slope for this mechanism is 2.3RT/PF, and this is one of the few cases offering good evidence that P = a, namely, that the experimentally measured transfer coefficient is equal to the symmetry factor. A plot of log i versus E for the hydrogen evolution reaction (h.e.r.), obtained on a dropping mercury electrode in a dilute acid solution is shown in Fig. 4F. The accuracy shown here is not common in electrode kinetics measurements, even when a DME is employed. On solid electrodes, one must accept an even lower level of accuracy and reproducibility. The best values of the symmetry factor obtained in this kind of experiment are close to, but not exactly equal to, 0.500. It should be noted, however, that the Tafel line is very straight that is, P is strictly independent of potential over 0.6-0.7 V, corresponding to five to six orders of magnitude of current density. 

The distance decay constant / (see below) in Miller et al. s original study was 0.9 per CH2, using ferricyanide and iron(IH) hexahydrate [44]. In a later study which accounted more thoroughly for double layer effects, 2 was determined to be 1 eV for kinetically facile redox probes such as ferricyanide, 1.3 eV for Ru-hexamine and 2.1 eV for iron(III) hexahydrate. With a better understanding of the redox probe behavior, f was found to be 1.08 + 0.20 per CH2 and independent of the redox couple and electrode potential [96]. Pre-exponential factors were also extracted from the Tafel plots. The edge-to-edge rate constants (extrapolated) are approximately 10 -10 s for all redox probes, which is reasonable for outer-sphere electron transfer. The pre-exponential factors are 5 x lO s [96]. 

The formulation in Eq. (110) shows that the apparent heterogeneous rate constant k(E) depends on the potential. This dependence has been observed experimentally since the earliest times of electrode kinetics and is at the origin of the so-called Tafel plots [83]. Indeed, when the potential E is sufficiently different from E°, for example nF(E — E°) 0, the term relative to (P)o in Eq. (109) vanishes and the current is given... 

Fig. 17.2 Tafel plots for the (normalized, dimensionless) current, yjy, that accompanies hydrogen evolution in a solution containing 3.4 mM HCl + 1.0 M KCl, corrected for diffuse-double-layer effects, mass transport controlled kinetics and ohmic potential drop, measured at three temperatures (5, 45, 75°C all results fall on the same line of this reduced plot) at a dropping mercury electrode. The slope obtained from this plot is 0.52, independent of temperature. (Based on data from E. Kirowa-Eisner, M. Schwarz, M. Rosenblum, and E. Gileadi, J. Electroanal. Chem. 381, 29 (1995) and reproduced by the authors.)...

A rotating platinum disk electrode was used for gathering data for the calculation of the kinetic constants. Tafel plots (5) were developed (Figure 2), from which the heterogeneous rate constants, k , and the electron-transfer coefficients, a, were determined. In all determinations of kinetic parameters, a blank voltammogram, run under identical conditions, was subtracted from the data to remove current due to background reactions or charging of the double layer. 

Table H. Heterogeneous electron-transfer kinetics at the platinum disk electrode at 298 K. All values determined from linear portions of Tafel plots at rates of rotation extrapolated to infinity. Reaction of Se and As too slow for observation...

To understand more quantitatively the dependence of the corrosion potential and current on the kinetic parameters of the two electrode processes (9.3) and (9.5), the I-E data of Fig. 9.2 should be replotted in a semi-logarithmic form, i.e. as a Tafel plot (Fig. 9.3). A linear Tafel line will only be observed in the potential range where a single electrode process predominates. However, these Tafel lines can be extrapolated to the corrosion potential and if necessary (as in the figure) also to the calculated equilibrium potentials for the H2O/H2 and M/M couples where the exchange currents are I and respectively. The equations for the two... 

Experimental kinetic measurements at SAM-coated electrodes yield two parameters, the standard rate constant and the reorganization energy X. The latter can be obtained either by measuring the rate constant versus the overpotential and fitting a Tafel plot to the theoretical curves or by meastiring the standard rate constant versus temperature and using Eq. (8). Once... 

As in /l, the last term in Eq. (47) vanishes and c,Fe = 1 - h. From the measurements of hydrogen evolution kinetics in the same system, the transfer coefficient an was fotind to be 0.51. Hence, ac,Pe = 0.49 and the cathodic Tafel line would have a slope of 2RT/F (shown in Figure 10 in the form of the corrected Tafel plot), if the pH in the vicinity of the electrode were constant with changing current density. Considering this result, as well as the reaction order of 1 for OH ions, mechanism (38) is indicated for the deposition and dissolution of iron, with FeOH as the electroactive species and its discharge as the rds. 

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